Non compact conformal field theory and the $a_2^{(2)}$ (Izergin-Korepin) model in regime III

Eric Vernier (1) , Jesper Lykke Jacobsen (2) , Hubert Saleur (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay

The so-called regime III of the $a_2^{(2)}$ Izergin-Korepin 19-vertex model has defied understanding for many years. We show in this paper that its continuum limit involves in fact a non compact conformal field theory (the so-called Witten Euclidian black hole CFT), which leads to a continuous spectrum of critical exponents, as well as very strong corrections to scaling. Detailed numerical evidence based on the Bethe ansatz analysis is presented, involving in particular the observation of discrete states in the spectrum, in full agreement with the string theory prediction for the black hole CFT. Our results have important consequences for the physics of the O(n) model, which will be discussed elsewhere.

Domains: Statistical Mechanics [cond-mat.stat-mech]; Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur. Non compact conformal field theory and the $a_2^{(2)}$ (Izergin-Korepin) model in regime III. Journal of Physics A: Mathematical and Theoretical, 2014, 47 (28), pp.5202. ⟨10.1088/1751-8113/47/28/285202⟩. ⟨cea-01065510⟩